Single replicate factorial designs for incomplete block experiments are obtained by first constructing a single replicatepreliminary designin incomplete blocks for the same number of factors but an excessive number of levels of the first factor, then deleting the excess treatment combinations to obtain adeletion design.Any single replicate preliminary design yields a single replicate deletion design. Furthermore, if the preliminary design is orthogonal, then the resulting deletion design is shown to be nearly orthogonal and, under certain reduced models, to provide efficient estimation of lower-order effects and in some cases an orthogonal analysis. For example, a 2×32deletion design is constructed in three blocks of size 6, the 2 df confounded being the sum of interaction effects ofF2andF3and second-order interaction effects. If second-order interactions are assumed negligible, then the deletion design provides efficient estimation of interactions betweenF2andF3and an orthogonal analysis. In another example, a 2×32deletion design is constructed in nine blocks of size 2 with main effects ofF1unconfounded. In a main-effects model, main effects ofF2andF3are estimable with optimal average efficiency. Experimental settings involving more factor levels are also considered, tables are given showing the efficiency of the resulting deletion designs to compare favorably with optimal upper bounds, and the deletion designs are shown by comparison to be more efficient on lower-order effects than competing orthogonal designs.